It is well-known that, if the thickness of a material is known, one can determine the average density of a material by using radiation beams that are absorbed by the same material. The absorption is a function of the mass absorption coefficient, A, which depends on the type of material. Therefore, the density is proportional to the attenuation of the radiation, in photons X or γ, through the material and can be measured directly provided the thickness is known and the material is homogeneous.
The “Compton scattering technique” is also known for determining the density of a material. With this technique, the density distribution of a material is examined by passing a collimated beam of photons through the material and analyzing the radiation that is scattered by the same material. This measurement does not depend on the thickness of the material.
As is well known in quantum physics, according to the Compton effect, the trajectory and energy of a photon changes when said photon interacts with an atom. Under the Compton effect, the difference of energy of the photon before the interaction and after the interaction is responsive to the direction of the new photon with respect to the direction of the primary photon. As is known, the energy is inversely proportional to the wavelength, and the variation of wavelength derives from the known Compton equation:             λ      ′        -    λ    =                    h                  m          ⁢                                           ⁢          c                    ⁢              (                  1          -                      cos            ⁢                                                   ⁢            θ                          )              =                            2          ⁢          h                          m          ⁢                                           ⁢          c                    ⁢                                    sin            2                    ⁡                      (                                          1                2                            ⁢              θ                        )                          .            where h is Planck's constant, c is the speed of light, m is the mass of an electron and θ is the angle of diffusion. From this equation, it is clear that it is important to know the energy of the incident photon in order to determine the energy of the photon after the interaction with the detected material at a suitable angle θ. However, it is not easy to know a priori the energy of the incident photon if it is produced by a radiation source, since an X-ray tube emits photons with a very extended spectrum range. In turn, the photon produced under the Compton effect will undergo further interactions within the same material and before it is detected. In particular, it can be attenuated along the chosen direction within a probability range.